Large Frequency Drifts During Type I X-Ray Bursts

A&A 410, 967–973 (2003) Astronomy DOI: 10.1051/0004-6361:20031310 & c ESO 2003 Astrophysics

Large frequency drifts during type I X-ray bursts

V. Rezania? and S. Karmand

Institute for Advanced Studies in Basic Sciences, Gava Zang, Zanjan 45195, Iran

Received 26 March 2003 / Accepted 21 August 2003

Abstract. We study the spin-down of a neutron star atmosphere during the type I X-ray burst in low mass X-ray binaries. Using polar cap acceleration models, we show that the resulting stellar “wind” torque on the burning shell due to the ﬂowing charged particles (electrons, protons and ions) from the star’s polar caps may change the shell’s angular momentum during the burst. We conclude that the net change in the angular momentum of the star’s atmosphere can account for rather large frequency drifts observed during type I X-ray burst.

Key words. stars: neutron – stars: magnetic ﬁelds – X-rays: binaries – X-rays: bursts

1. Introduction alone cannot account for explaining rather large frequency drifts (∆ν/ν 1.3%) observed in some bursts (Galloway The discovery of high coherence, large modulation ampli- 0 et al. 2001; Wijnands∼ et al. 2001). As pointed out by Galloway tudes, and stable frequency oscillations in the range ν 0 et al. (2001), the required expansion by these frequency drifts 270 620 Hz during type I X-ray bursts in weakly-magnetic∼ is 4–5 times larger than the one predicted by Cumming & (B − 1010 G) accreting (at intermediate rate 10 11 M yr 1 < − − Bildsten (2000), see Table 1. In order to achieve the rather large ˙ ≤ 8 1 M < 10− M yr− ) neutron stars in low mass X-ray bi- frequency shift, Cumming et al. (2001) improved the calcula- naries (LMXBs) has issued many new puzzles for investigations done by Cumming & Bildsten (2000) by including the tors. An initial puzzle seen in the observations was that the general relativistic corrections for either slowly or rapidly ro- oscillation frequency increases by ∆ν a few Hz during the tating star. They found that the general relativity has small ef- burst. Strohmayer et al. (1997) firstly∼ proposed that this fre- fect on the angular momentum conservation law ( 5 10%). quency shift is due to the conservation of angular momen- Comparing with the data, for a rigidly rotating atmosphere,∼ − tum of the decoupled burning shell from the neutron star in they obtained that the expected spin-down is a factor of two which the shell undergoes spin changes as it expands and con- or three less than the actual observed values. In another at- tracts during the type I X-ray bursts. Motivated by this pro- tempt, Spitkovsky et al. (2001) considered a two-dimensional posal, Cumming & Bildsten (2000) studied the rotational evo- hydrodynamics model that the burning spots can spread over lution of the neutron star atmosphere during a thermonuclear the neutron star surface. Due to the combination of the radial burst by considering one-dimensional vertical hydrostatic ex- expansion of the burning shell and rotation of the star, they pansion. By assuming conservation of the angular momentum proposed that horizontal hydrodynamics flows may arise in the of the shell, they showed that a hot burning shell might expand neutron star burning ocean during the type I X-ray burst. By hydrostatically by ∆R 20 m (Ayasli & Joss 1982; Hanawa & taking into account the action of the Coriolis force due to the Fulimoto 1984; Bildsten∼ 1998), and lag behind the neutron star rapid rotation of the star, they showed that the horizontal flows by ∆ν ν (2∆R/R) 1Hz(ν /300 Hz)(∆R/20 m)(10 km/R) s s may explain many features of observed bursts such as the very where ν∼ is neutron star∼ spin frequency and R the radius. As the s short rise time of X-ray bursts and the lack of burst oscillations shell cools down and contracts, the rising oscillations due to in several bursts. Further, they argued that during cooling the a temperature inhomogeneity, drifts upward as we seen by ∆ν hot ashes left by burning front, there is temperature gradient of few Hertz. By assuming that the burning shell rotates rigidly, between equator and pole, increasing toward the pole, which they found rough agreement with the observed values with frac- drives a zonal thermal wind directed backward to the neutron tional frequency shifts ∆ν/ν 0.8%. 0 ≤ star rotation. 1 They found that only if the frequency drift due However, recent observations suggested that purely radial to the radial expansion is combined with the geostrophic drift hydrostatic expansion and angular momentum conservation

Send oﬀprint requests to: V. Rezania, 1 Actually they showed that due to the hydrostatic balance the ma- e-mail: [email protected] terial will likely ignite sooner at the equator rather than the pole. As a ? Present address: Department of Physics, University of Alberta, result, one would expect the burning front cools down at the equator Edmonton AB, Canada T6G 2J1. ﬁrstly.

Article published by EDP Sciences and available at http://www.aanda.org or http://dx.doi.org/10.1051/0004-6361:20031310 968 V. Rezania and S. Karmand: Large frequency drift during type I X-ray bursts

Table 1. In this table we obtain the lowest radius expansion ∆R (based on hydrostatic expansion models) and the scaled magnetic ﬁeld ηB (based on the polar cap particle acceleration models) for some X-ray bursts in LMXBs. We calculate these quantities for two chosen values of the star spin frequency, νs = 300 Hz and νs = 600 Hz, such that the corresponding frequency shift is comparable with observations. ν0 is the oscillation frequency and ∆ν its corresponding shift seen during the burst. The value of ηB is based on the assumed value of ∆R 20 m for ' both spin frequencies, see Eq. (9).

Object Time ν0 ∆ν/ν0 ∆R300 ∆R600 (ηB)300 (ηB)600 3 10 10 (UT) (Hz) (10− )(m)(m)(10G) (10 G) 4U 1636-54 1996 Dec. 28 (22:39:22)1,2 580.5 2–4 40 20 3 1 ∼ ≥ ≥ ≥ ≥ 1996 Dec. 29 (23:26:46)2,3 581.5 3 40 20 2 0.01 ∼ ≥ ≥ ∼ ≤ 1996 Dec. 31 (17:36:52)2,3 581. 3 40 20 2 0.01 ∼ ≥ ≥ ∼ ≤ 4U 1702-43 1997 Jul. 26 (14:04:19)4 329.85 0.1 7.7 0.3 50 – 6– ± ± ≥ ≥ 1997 Jul. 30 (12:11:58)4 330.55 0.02 4.8 0.3 30 – 2– ± ± ≥ ≥ 4U 1728-34 1996 Feb. 16 (10:00:45)4,5 364.23 0.05 6.6 0.1 50 – 5– ± ± ≥ ≥ 1997 Sep. 9 (06:42:56)4 364.10 0.05 5.9 0.2 45 – 4– ± ± ≥ ≥ Aql X-1 1997 Mar. 1 (23:27:39)6,7 549.76 0.04 4.3 50 25 3 1 ± ≥ ≥ ≥ ∼ 4U 1916-053 1998 Aug. 1 (18:23:45)8 269–272 13.0 70 – 12.5 – ≥ ∼ MXB 1658-298 1999 Apr. 14 (11:44:52)9 567 9.0 100 50 10 7.5 ≥ ≥ ∼ ∼ References: (1) Strohmayer et al. (1998); (2) Miller (2000); (3) Strohmayer (1999); (4) Strohmayer & Markwardt (1999); (5) Strohmayer et al. (1996); (6) Zhang et al. (1998); (7) Fox et al. (2000); (8) Galloway et al. (2001); (9) Wijnands et al. (2001).

9 caused by backward zonal flows, one may expect to observe light cylinder (of radius rlc 5 10 /νs cm, where νs in Hertz), the rather large frequency drifts of burst oscillations in tails of and form a relativistic stellar∼ wind.× Several kind of acceleration some bursts. mechanisms has been developed (Mestel 1998), however, the Because of no coherent pulsations seen in persistent emis- one proposed by Arons (1979, 1981) may apply likely to X-ray sion from the majority of neutron stars in LMXBs, it is be- burst pulsars that we will consider here. Arons assumed that lieved that they are weakly magnetized (B 109 G). So, in charged particles (electrons and ions) flow freely from the neu- previous studies the effect of magnetic field of≤ the neutron star tron star surface due to the thermal activities. Freely escaping was ignored in the rotational evolution of burning atmosphere particles from the neutron star surface depends on the bind- during the X-ray bursts. In this paper we study the change in ing energy (referred as the cohesive energy for ions and as the the angular momentum of the burning shell during the type I work function for electrons) and the surface temperature. For X-ray burst. This study is based on polar cap particle acceler- typical magnetic field of a neutron star in LMXBs ( 108 G), ∼ ation models in the pulsar polar cap regions. Due to the star’s the threshold temperature for thermionic emission of electrons rotation and magnetic field an electric field must be induced in is T 104 K and for ions is T 103 K (Luo et al. 2000) that e ∼ i ∼ magnetosphere, i.e. E = (Ω r) B/c, that has non-zero are 104 105 lower that surface temperature of the neutron star s − component along the magnetic− field× lines× (E = E B)(seefor in LMXBs. Further, due to the thermonuclear activities on the || · recent review Mestel 1998). Ωs is the angular velocity of the surface of the star during the X-ray burst, the particles’ kinetic star, and r is a distance outside of the star. The parallel elec- energy would increase significantly. Therefore, freely flowing tric field accelerates charged particles along the open magnetic particles is very likely from the surface of such a pulsar. field lines above the polar caps up to ultrarelativistic energies Outward flowing charged particles above the pul- toward the star’s light cylinder (rlcΩs = c). Here, we argue that, sar polar caps along the open magnetic field lines 8 for typical magnetic field B 10 G, the net charged particles causes the Goldreich-Julian (corotation) charge den- flowing from star surface to∼ infinity in the pulsar polar caps, sity ρGJ Ωs B/2πc cannot be kept balanced (Harding would exert a stellar wind torque on the burning shell that may & Muslimov∼ 1998).· As a result, a strong electric field de- cause the angular momentum of the shell to change during the velops along the magnetic field, E , above the magnetic burst. We show that the net change in the angular momentum of || poles due to the departure of total charge density ρe from the shell during the burst can account for rather large frequency the Goldreich-Julian charge density, starts from zero at the drifts of burst oscillations. surface and grows with distance above the surface. Even though ρe = ρGJ, and therefore E = 0 at the surface, the || 2. The model curvature of the field lines causes the area of the open-field region to increase, so that ρe increases faster than ρGJ,andthen The theory of particle acceleration in pulsar magnetosphere a charge deficit grows with distance (Harding & Muslimov has been studied for three decades, after pioneering work 1998). Calculation of the parallel electric field is so com- by Goldreich & Julian (1969) on pulsar electrodynamics. plicated and depends on several mechanisms that work to The charged particles accelerated by the parallel electric field enhance or screen the field. In a series of papers Harding & (relative to the magnetic field lines) escape from the surface Muslimov (1998, 2001, 2002); and Harding et al. (1998) along the open field lines which extended beyond the star’s have extensively studied the influence of pair production, V. Rezania and S. Karmand: Large frequency drift during type I X-ray bursts 969 inertial frame-dragging effect, curvature radiation, and inverse neutron stars in LMXBs with an ocean of accumulated hot mat- Compton scattering on the E . They showed that for the unsat- ters, the value of η must be greater than 1, due to the free ejec- || 1/2 urated region with altitude in range 0 < z (ΩsR/c) 0.1 tion of particles from the front surface of the ocean. Further, 6 ' 8 (for Ωs = 600π(νs/300 Hz) rad/sandR 10 cm) above during bursting the accumulated materials with T 10 Kon the stellar surface, the parallel electric field∼ grows linearly the neutron star surface, the kinetic energy of particles≥ inside with height as E (θ, φ, z) = E0(θ, φ)z, while for the saturated the ocean abruptly increases and then, the space charge density || 1/2 region with z > (ΩsR/c) , the parallel electric field that is would increase significantly in regions with non-zero parallel nearly constant respect to the altitude, drops by three order of electric field. As a result, one would expect that the number par- magnitudes. Here θ and φ are spherical polar and azimuthal ticles that may leave the shell would increase during the burst. angles, and z is the altitude in units of stellar radius. The It is necessary to note that for neutron stars in LMXBs 11 1 amplitude E0(θ, φ) depends on magnetic field strength B,spin with intermediate accretion rate, 10− M yr− < M˙ < 8 1 frequency νs, and orientation of the magnetic field symmetric 10− M yr− , the existence of pulsar wind torque might not axis relative to the star spin axis χ. In a simple form, one can be consistent with accretion. One would expect the motion of estimate E when the charged particles flow freely from the the accreting materials to oppose and shut off the radio pul- || neutron star surface (see Arons 1981; Usov & Melrose 1995; sar wind, and contribute to the angular momentum of the sys- Harding & Muslimov 2001) as tem. This scenario is unlikely “during the X-ray burst” due to the following reasons: before the burst the accretion disk ν 5/2 R 5/2 E 8.2 105 V/m s extends down to the neutron star’s surface. When the burst || ' × 300 Hz 106 cm stars, a huge thermonuclear explosion on the surface of the B z star causes the explosive eruption of the accumulated materi- . (1) als from the surface during the burst with bulk velocity close × 108 G 10 4 − to the speed of light. The resulting luminosity due to the ex- Note we calculated E here for a typical neutron star in LMXBs plosion exceeds the Eddington limit at this time. As a result, with nearly perpendicular|| field orientation relative to the spin the inner part of the accretion disk is swept away by the burst axis. The relative fraction of electric force to the gravity force radiation pressure. As a result, one would expect the action 3 above the burning front during the burst, i.e. z 10− ,for of accretion to more or less shut off in this period due to the electrons and protons are 8 104 and 42, respectively.∼ As strong interaction of the expanded shell with the inner accre- a result, electrons, protons,∼ and× even ionized∼ helium atoms can tion disk. Interestingly, Shaposhnikov et al. (2003) used the be accelerated easily along the magnetic field lines by paral- latter mechanism to explain why the emitted flux from neu- lel electric field presented in the polar caps of neutron stars in tron star in the X-ray source 4U 1728-34 is not constant during LMXBs. Since the magnetic field lines in the polar cap regions the expansion stage. Furthermore, it has been suggested the ac- are not closed and extended beyond the star’s light cylinder, tion of accretion torque is balanced by the gravitational radia- the accelerated particles in these regions may leave the neutron tion torque in neutron stars in LMXBs, see Bildsten (1998a, star magnetosphere. The resulting flow of particles from the 2002) for details. Therefore, the increased angular momen- polar caps to infinity produces a relativistic “stellar wind”, that tum due to accretion is lost to gravitational radiation. The exerts a “stellar wind torque” (Michel 1991) on the shell, and latter mechanism provides a natural explanation for the rota- then causes the net angular momentum of the shell to change tion of stars in a narrow range of frequencies, νs 300 Hz. ∼ 1/2 during the burst. The net wind torque exerted on the shell due Finally, the magnitude of accretion torque Ta M˙ (GMsR) 32 9 1 ∼ ' to the out flowing charged particles from the star polar caps 8.6 10 dyne cm (M˙ /10− M yr− ) (for Ms = 1.4 M is estimated by Michel (1991) for the Goldreich-Julian charge and ×R = 10 km) is one order of magnitude smaller than that 33 density to be of the wind torque Tw 9.32 10 dyne cm for η 1000 and B 108 G, see Eq. (3)∼ and the× discussion below Eq.∼ (9). 2 ∼ TW = I /4cΩs (2) By replacing I in Eq. (2) we obtain where I = ηn evA is the total current of the charged particles 2/3 GJ pc Ms − 3 27 2 flowing from the polar caps with the area Apc 1.6πR /Rc that Tw 9.32 10 dyne cm η 2 ≈ ' × 1.4 M ! is 10% of total star’s area (4πR ). Here nGJ 0.36ΩsB/2πec 8 8 3 ' ' 7/3 6 2 7.5 10 (νs/300 Hz)(B/10 G) cm− is the Goldreich-Julian νs R B × 10 2 1/3 charge number density, e = 4.8 10 esu, R = (GM /Ω ) 8 (3) × − c s s × 300 Hz 10 km 10 G · is the corotation distance for a star with mass Ms,andv 0.1c 3 ≥ is average speed of particles at z 10− . The velocity of parti- Equation (3) gives the exerted torque on the neutron star sur- cle grows up quickly to c at z ∼0.1 as it is accelerated by E . face due to the flowing charged particles from the pulsar polar η 1 is a dimensionless∼ factor∼ (free parameter of the model)|| caps. Therefore, the burning shell of the neutron star will ex- ≥ such that the quantity ηnGJ represents the actual number density perience this torque as it expands during the burst. The angular of particles that accelerated and left the star due to the parallel momentum of the shell at a distance R from the center of the electric field. The value of η 1 for old and isolated neutron star in Newtonian dynamics can be written as stars (with no observed bursts),' i.e. the space charge density is nearly Goldreich-Julian charge density for these stars. But in ` = κMR2Ω, (4) 970 V. Rezania and S. Karmand: Large frequency drift during type I X-ray bursts

2 where constant κ = (I/MR )shell depends on the equa- 2.2. The rising time tion of state and κ 2/3 (an uniform spherical This period starts with abruptly thermonuclear ignition of the shell). Here M and I are≤ the mass and moment iner- accumulated hydrogens and heliums during the recurrence tia of the shell. Equation (4) may be corrected by ` = time. The burning shell expands in less than 1suptoz κMR2 sin2 θΩ /(1 2GM /R)1/2 for a relativistic spherical star s s 2 10 3 (Ayasli & Joss 1982; Hanawa & Fulimoto∼ 1984;' and by ` = κMR2 −sin2 θ(Ω ω)/(1 2GM /R)1/2 for a rotat- − s s Bildsten× 1998). In this period, as in the hydrostatic models, we ing relativistic star (see Cumming− et− al. 2001). Here ω = J /R3 s assume that the rotational evolution of the expanding shell is where J is the total angular momentum of the star. However, s nearly independent of the star itself. as shown by Cumming et al. (2001), the relativistic corrections have small contributions to the final results, and so we ignore As we mentioned before, in this period due to the huge them. The time evolution of the angular momentum of the shell thermonuclear explosion on the surface of the star, the ac- will be cumulated materials are explosively erupted out of the star with a mass bulk velocity close to the speed of light. The ∆ 2 outgoing plasma density within period of time ∆t 1s,is (R Ω)shell = Tw/κM, (5) ∆t − [(A /4πR2)M ]/A that is 10 times (or more) larger∼ than ∼ pc shell pc or infalling plasma density macc/Apc due to the accretion flow at the same period of time (note that as mentioned by Strohmayer (R2Ω) (2∆R/R +∆Ω/Ω) = (T /κM)∆t. (6) shell shell − w & Bildsten (2003), the bursts occur when the accretion rate is 10 1 Therefore, the change in the angular velocity of the burning clearly less than 10− M yr− .). Here macc = M˙ ∆t is the av- shell will be erage mass of accreting materials during ∆t. As a result, the expanding shell sweeps away the inner part of accretion disk (∆Ω/Ω) = 2∆R/R (T /κMR2Ω) ∆t. (7) shell − − w and then one would expect the action of accretion to more or Here we assumed that the change in the mass of the shell less shut off during this period. 2 The parallel electric force at height z 2 10 3 is 80 times is order of or less than (∆R/R) and then we neglect it (see ' × − Cumming et al. 2001). Equation (7) represent the change in bigger than gravitational force for hydrogen atoms, see Eq. (1). angular velocity of the shell during the burst. Now we discuss Therefore, the charged particles that rise with the expanding the change in angular velocity in three stages, before the X-ray shell will be accelerated toward the outside of light cylinder by burst or the recurrence period, the rising period, and after the the strong parallel electric field along the open magnetic field burst. lines. Further, the sudden thermonuclear explosion of the accumulated materials in the ocean causes the thermal energy of the charged particles to increase. Consequently, we expect that 2.1. Before the X-ray burst the number density of particles that may leave the magneto- In this period the neutron star accrets materials from its com- sphere ηnGJ in this period increases significantly. The resulting wind torque for η 103 will give a net change in angular ve- panion star and accumulates them in the ocean that more or less ∼ rigidly corotates with the star (Cumming et al. 2001). The par- locity of the shell as allel electric field inside the ocean is nearly neutralized due to ∆Ω redistribution of charge particles of the ocean. Further, due to = 2 ∆R /R (T /κMR2Ω) ∆t, Ω w the large plasma density of infalling matters, the electric field !shell − | | − outside of the ocean would be shorted out. Therefore, the po- 3 z 2 10− 3 lar cap acceleration is more or less suppressed due to strongly '− × 10− 2 2/3 1 accreting plasma in this period. As a result, the pulsar wind 3 η Ms − M − 7.42 10− torque would be negligible. − × 103 1.4 M ! 1021 g! Furthermore, because of nearly rigid rotation of the ocean 4 4/3 2 R νs B ∆trise with star the net wind torque (if exists) during this period will , (9) × 10 km 300 Hz 108 G 1s ! be acted more or less on the star itself. Therefore, Eq. (7) should be corrected for this period as where κ = 2/3and∆R 10 m is the average change in thickness of the burning shell' during a burst. For η 103 and ∆Ω 2 8 11 ∼ = (T /κ0 M R Ω) ∆t, B 10 G(ηB 10 G), the net change in angular velocity Ω w s !shell − of∼ the shell given∼ by Eq. (9) is in good agreement with large 2 5/3 3 17 η Ms − frequency shifts seen in observations. We note that for η 10 , 4.44 10− ∼ 2 '− × 100 1.4 M ! the number of particles that left the star ∆N 4πηnGJR ∆R ∼ 4 4/3 2 is much smaller than total number of particles in the ocean R νs B ∆trec , (8) N M/m ,i.e.∆N/N 10 17. As a result, the change in the × 10 km 300 Hz 107 G 104 s! p − mass∼ of the shell (∆M/M') is negligible. In Table 1 we calculate that is extremely small. Here ∆trec is the burst recurrence time the quantity ηB for both 300 Hz and 600 Hz spin frequencies and κ0 = 2/5. As is clear, the net wind torque on the shell/star (for those which applicable), to produce the frequency shifts in this period and so the change in angular velocity of the observed in various systems. As a result, the suggested mag- shell/star is negligible. netic fields are in range 1 10 108 Gforη 100 1000. This − × ∼ − V. Rezania and S. Karmand: Large frequency drift during type I X-ray bursts 971

Before the burstburst After the burst Ω s ∆Ω

(Cumming et al 2001)

∆Ω

(Particle wind model)

Fig. 1. In this figure we schematically compare the change in angular velocity of the expanding shell and then oscillations’ frequency during the type I X-ray burst suggested by Cumming et al. (2001) (dotted line) and the one proposed here (solid line). Due to the exerted torque on the shell by the particle wind from the magnetic polar cap regions during the burst, we expect a larger depth in ∆Ω rather than the model discussed by Cumming et al. (2001). As a result, the larger drift would be expected in the burst tail. The solid and dotted curve after the burst are drawn schematically to show star-shell recoupling in this period. is consistent with other observational evidences about the mag- the various mechanisms such as magnetic field winding, see for netic field of neutron stars in LMXBs. more detail Cumming & Bildsten (2000). The angular velocity 12 of the star changes by δΩs = (M/Ms)∆Ω 10− ∆Ω which is negligible. As a result, one would expect' that the oscillations’ 2.3. After the X-ray burst frequency will increase as the shell spins up by ∆ν/ν ∆Ω/Ω. 0 ∼ At final stage, after the thermonuclear flash, the expansion will Interestingly, the magnetically recoupling of the star-shell sys- be stopped by the star’s gravity force, and then the expanded tem may explain why the burst oscillations, as seen in the ob- shell starts to contract as they cool down. Because of the charge servations, reach to their maximum frequencies (i.e. the star redistributions during the expansion, the original induced elec- spin frequency) before the shell completely contracted. tric field is neutralized inside the expanded shell. So the mag- In Fig. 1, we compare the corresponding changes suggested nitude of the parallel electric field inside the ocean will drop by previous studies (Strohmayer et al. 1997; Cumming et al. to zero, and then the electrostatic acceleration will cease inside 2001) and the one we discussed here. As is clear, due to the the ocean. Due to the lack of outward electrostatic accelera- exerted torque by the particle wind in polar cap regions, the tion, the ocean’s particles are mostly accelerated downward by shell’s spin frequency, and then the oscillations’ frequency de- strong gravity. Furthermore, the action of accretion plasma is crease more than in the calculation by Cumming et al. (2001) starting to recover, and as a result, the polar cap acceleration during the rising time. Therefore, we expect to observe larger will shut down in this period. Although, because of new charge change in oscillations’ frequency during the burst tail. distribution, a new parallel electric field may develop above the burned front we expect that the polar cap particle acceleration 3. Discussion mechanism is more or less unlikely after the burst. As a result, the number of particles that may leave the star will decrease Among the 50 known Galactic LMXBs, the highly coherent as well, i.e. η 10. Further as the shell cools down, it gets burst oscillations∼ with large modulation amplitudes and stable ≤ closer and closer to the star, and then its coupling to the star frequencies in range ν0 270 620 Hz are seen in ten LMXBs gets stronger and stronger. This can be understood by noting during type I X-ray bursts.∼ These− oscillations are most com- the magnetic field near the star’s surface opposes the differen- monly seen during tails of bursts, when the burning is thought tial rotation arising between shell and surface of the star during to have spread over the whole surface and obviously asymme- the burst (otherwise the magnetic field inside of the shell will try is no longer present, are not observed in all type I X-ray be wound up and intensified due to the shearing layers – the bursts from the same source. While it is believed that the os- winding of the magnetic field). Therefore, the net wind torque cillation frequency is closely related to the neutron star spin will be acting more and more on the whole star again rather frequency due to the observation of the kHz quasi-periodic os- than shell itself, and so we can neglect it, see Sect. 2.1. cillations in the persistent emission (van der Klis 2000), there The magnetic recoupling of the shell forces the shell to spin is still an ambiguity that whether the oscillation frequency is up until it achieves the star’s spin frequency. The shell gains its the spin frequency or twice the spin frequency. Further, as 2 angular momentum deficit (MR ∆Ω)shell, from the star through seen in observations, the oscillation frequency increases by ∆ν 972 V. Rezania and S. Karmand: Large frequency drift during type I X-ray bursts a few Hz during the burst. This frequency shift is firstly ex- distributions and screen the electric field (see for more detail plained by Strohmayer et al. (1997) that the burning shell de- Harding & Muslimov 2001). In millisecond pulsars (with no couples from the star, and undergoes spin changes due to the burst activities) the polar cap particle acceleration mechanism conservation of angular momentum of the shell as it expands was studied by Luo et al. (2000). They showed that in these and contracts during the type I X-ray bursts. Further observa- pulsars this mechanism, which is relatively efficient in acceler- tions and studies suggested that purely radial hydrostatic ex- ating charged particles in the star’s polar caps, mostly suffers pansion and angular momentum conservation alone cannot ex- energy loss from the radiation of accelerated particles along plain rather large frequency drifts (∆ν/ν 1.3%) observed the field lines (curvature radiation). So the maximum energy in some bursts (Cumming et al. 2001; Galloway∼ et al. 2001; attainable by the particle is limited by energy loss through the Wijnands et al. 2001). For recent review on the thermonuclear radiation reaction. They found that the maximum Lorentz fac- bursts and their properties see Strohmayer & Bildsten (2003). tor that might be achieved by an individual particle at z 0.1 2 1/4 7 ∼ In this paper, we addressed the latter problem by studying is Γ=(6πε0E ρc /e) 10 , however, the Lorentz factor for the evolution of angular momentum of the burning shell during the bulk pair plasma|| is much∼ smaller 100. The latter may ex- the type I X-ray bursts in LMXBs. Based on particle acceler- plain the lack of detection of high energy∼ γ-rays in these stars. 1/2 ation models near a pulsar polar cap region (Mestel 1998), we Here E is given by Eq. (1) and ρc (4/3)(cR/2πνs) 4|| 1/2 6 ∼ ∼ studied the change in the angular momentum of the burning 5 10 (300 Hz/νs) (R/10 cm) m is the curvature radius of shell during the type I X-ray burst. The net charged particles the× field lines. that accelerated by parallel electric field in star’s polar caps, For neutron stars in LMXBs with intermediate accretion flow from the star surface to infinity through open magnetic rate, however, the polar cap acceleration mechanism mostly field lines, would exert a torque on the burning shell (called suffers from the action of accretion plasma. Because of the wind torque) and cause the angular momentum of the shell large plasma density (macc/Apc) of the accretion flow toward changes during the burst. We introduced a dimensionless fac- star’s polar caps, the parallel electric field in the polar cap tor η that the quantity ηnGJ represent the number density of the regions would be shorted out and the polar cap acceleration ejected particles from the burning shell above the pulsar polar mechanism would be suppressed. We note that, this scenario is caps. We showed that for η 100 1000 (during X-ray bursts) not likely during X-ray bursts due to the explosive eruption of and a typical magnetic field∼B −1 10 107 G in the pulsar materials from the surface and possible evacuation of part of polar caps, the rather large observed∼ − frequency× drifts of burst inner disk. In this period with ∆t 1 s, the eruptive plasma oscillations can be explained by the resulting wind torque ex- density is 10 times larger that the accreting∼ plasma density, i.e. 2 erted on the burning shell. In Table 1, we obtained the values [(Apc/4πR )Mshell]/Apc 10 macc/Apc. for ηB for both 300 Hz and 600 Hz spin frequencies that causes ∼ It is necessary to note∼ that the polar cap acceleration mecha- the corresponding frequency drift observed in each burst. As is nism requires the observation of radio pulsed signals from neu- clear, the resulting magnetic fields’ strength is in a good agree- tron stars in LMXBs. Recently Burgay et al. (2003) carried out ment with other observations from the neutron stars in LMXBs, observations, searching for radio pulsed emission at 1.4 GHZ such as the lack of coherence pulsations in persistent emission. from six soft X-ray transient sources (weakly magnetic accret- Above the neutron star’s polar caps particles flow outward ing neutron stars) during their X-ray quiescent phase. No such along the open magnetic field lines and a steady charge density a signal was detected. However, they discussed several mech- cannot be maintained at the Goldreich-Julian density every- anisms such as free-free absorption from the ejected materials where. Consequently, a strong electric field develops along the during the burst that can hamper the detection and explain the magnetic field, extracts the “primary” charged particles with null result. In particular, they showed that during the quiescent, density n nGJ (for a star with no burst activity, see Sect. 2) the amount of the gas lost by the neutron star’s companion is in- from the surface∼ and accelerate them to high Lorentz factor sufficient to quench the radio emission, but is sufficient to com- ( 107). According to the polar cap models, the predicted ra- pletely absorb the radio signal. Therefore, one cannot generaly diation∼ luminosity for a typical millisecond pulsar would be rule out the polar cap acceleration mechanism (and its resulting 33 5/28 8 1/7 10 (νs/300 Hz) (B/10 G)− ergs/s that is compa- pulsar wind) based on the lack of the radio pulsed signals from rableE∼ to γ-ray luminosities. So, one may expect to observe these sources. However, further observartions, particularly dur- γ-rays in millisecond pulsars that has been detected only in ing the burst activity, are needed to be done in order to decide PSR J0218+4232 by EGRET (Kui et al. 2000). However, po- such a mechanism is irrelavent or not. lar cap particle acceleration is limited by various energy loss Finally, it is interesting to mention that the very recent mechanisms such as curvature radiation, resonant and nonreso- observation done by Chakrabarty et al. (2003) form the tran- nant inverse Compton scattering, and pair production. The ac- sient X-ray source SAX J1808.4-3658 shows that, as expected, celerated particles along the magnetic field lines suffer energy the burst oscillation frequencies are directly related to the star loss and emit photons through the curvature radiation. Further, spin frequency. However, it reveals some unusual behaviors these particles scattered by soft thermal X-ray photons emitted too. They observed a rather large frequency drift (∆ν 5Hz, from the hot surface and loss energy via inverse Compton scat- ∆ν/ν 1%) with a time scale one order of magnitude∼ faster tering. In addition, the high energy photons resulted from the than in∼ other neutron stars. Surprisingly, the oscillation reaches curvature radiation and/or inverse Compton scattering produce to its maximum frequency ( star spin frequency) during the ∼ a cascade of “secondary” e± pair particles with a number den- burst rise. This is completely inconsistent with conservation sity n 105n above polar cap region that change the charge of angular momentum of a expanding/contracting shell which e± ∼ V. Rezania and S. Karmand: Large frequency drift during type I X-ray bursts 973 requires the oscillation slows down (drifts from star spin fre- Ayasli, S., & Joss, P. C. 1982, ApJ, 256, 637 quency) during the burst rise. Bhattacharya, D. 1995, in X-ray Binaries, ed. W. H. G. Lewin, J. Although the magnitude of magnetic field of the neutron van paradijs, & E. P. 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